Consider a market demand curve that can be expressed as P = 300 - 3 Q. Each of t

Question

Consider a market demand curve that can be expressed as P = 300 - 3 Q. Each of the firms currently serving the market has a total cost function of the form C = 40 q so MC = ATC = 40. There are no fixed costs.

a. If the market is served by a (short-run) profit-maximizing monopoly, calculate P*, Q*, and profits for the monopolist. Show work.

b. If the market is instead served by a limit-pricing monopolist, calculate P*, Q*, and profits. Assume that each potential entrant has the total cost curve given by C = 105 q. Show work. If the discount rate is 10%, compute the present value of a stream of profits for 3 years for the limit-pricing monopolist of this question. Do not discount the first year’s profits. Show work.

c. Compared to the three-period limit-pricing strategy from part b, should the monopolist use a short-run profit-maximizing strategy instead if it can maintain its monopoly only for a single period? (After that, let’s assume that entry would force its profits all the way to zero.) Explain.

Explanation / Answer

monopoly equilibrium conditions are MR = MC

pQ=(300-3Q)Q= TR, MR= 300-6Q , MC=40 IN EQUILIBRIUM MR=MC, 300-6Q= 40 ,, Q=260/6= 43.33

P= 300-3Q= 300-3*43.33=170 (approx)

b). limit pricing monoPOLIST will charge a price less than 105 because any potential enterant will not sell below its marginal cost which is given 105

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